1. Field of the Invention
The present invention relates to quantum information processing, and, in particular, to techniques for performing logic operations using quantum states of single photons.
2. Description of the Related Art
The past approaches described in this section could be pursued, but are not necessarily approaches that have been previously conceived or pursued. Therefore, unless otherwise indicated herein, the approaches described in this section are not to be considered prior art to the claims in this application merely due to the presence of these approaches in this background section.
Information processing using classical computers relies on physical phenomena, such as magnetic fields, voltages, and optical intensity that can be produced and measured in each of two base states, one base state representing a zero and another base state representing a one. Each physical element that can achieve either of these two states represents one binary digit, called a bit. Quantum information processing uses physical elements that exhibit quantum properties that may include, not only one of the two or more base states, but also an arbitrary superposition state of the base states. A superposition state has some non-zero probability of being measured as one of the base states and some non-zero probability of being measured as another of the base states. A physical element that exhibits quantum properties for two base states represents one quantum bit, also called a qubit. Physical elements that are suitable for representing qubits include the spins of single electrons, electron states in atoms or molecules, nuclear spins in molecules and solids, magnetic flux, spatial propagation modes of single photons, and polarizations of single photons.
Logical operations performed on qubits apply not only to the base states of those qubits but also to the superposition states of those qubits, simultaneously. Quantum computers based on logical operations on systems of qubits offer the promise of massively simultaneous processing (also called massively parallel processing) that can address problems that are considered intractable with classical information processing. Such classically intractable problems that can be addressed with quantum computers include simulation of quantum interactions, combinatorial searches in unsorted data, finding prime factors of large integers, solving for cryptographic keys used in current secure communication algorithms, and truly secure communications (also called xe2x80x9cquantum cryptographyxe2x80x9d).
Obstacles to achieving quantum computers include the difficulty in isolating qubits from uncontrolled interactions with the environment and transmitting qubits. Many of the physical elements that represent qubits, such as molecules and solids, are not readily transmitted and interact strongly with their environment.
Single photons, however, interact little in many environments, including glass fiber and air, and are easily transmitted in such media. Therefore several approaches have utilized quantum properties of single photons.
One approach implements logical operations on single photons using non-linear interactions between single photons. A problem with non-linear interactions between single photons is that such interactions are very weak and no devices satisfactorily implement this approach.
Another approach uses linear interactions between single photons but relies on interferometer techniques, e.g., interference on two spatial modes of propagation for a single photon. For example, logic gates using this approach have been proposed by E. Knill, R. Laflamme, and G. J. Milburn, xe2x80x9cA scheme for efficient quantum computation with linear optics,xe2x80x9d Nature, vol. 409, p. 49, Jan. 4, 2001 (hereinafter Knill) and by M. Koashi, T. Yamamoto, and N. Imoto, xe2x80x9cProbabilistic manipulation of entangled photons,xe2x80x9d Physical Review A, vol. 63, 030301, Feb. 12, 2001 (hereinafter Koashi). These devices are called xe2x80x9cprobabilisticxe2x80x9d logical gates because they perform the desired logical operation in response to only a fraction of the input photons. However, it can be determined when an operation is performed successfully, so that, in a separate step often called a xe2x80x9cpost selectionxe2x80x9d step or a xe2x80x9cpost-detection selectionxe2x80x9d step, output photons are blocked unless the operation is successfully performed. It has been shown that the fraction can be increased close to a value of one with sufficient numbers of components and extra photons (called xe2x80x9cancillaxe2x80x9d) in particular states.
Probabilistic, linear devices proposed by Knill suffer from errors due to thermally induced phase shifts on the two spatial modes. Other probabilistic, linear devices proposed by Koashi reduce the phase shifts by including a large number of additional components and other resources, such as sources of a large number of qubits in particular states.
Based on the foregoing, there is a clear need for devices that perform logical operations on quantum states of single photons that do not suffer the disadvantages described above. In particular, there is a clear need for logical devices that operate on the polarization states of single photons that do not suffer thermally induced phase shifts and that do not require a large number of additional components and resources.
Techniques are provided for using quantum polarization states of single photons to perform logical operations. In one aspect of the invention, a logic device includes a first polarizing beam splitter that has first input spatial modes and first output spatial modes for a first set of orthogonal polarizations. A second polarizing beam splitter has a second input spatial mode and second output spatial modes for a second set of orthogonal polarizations different from the first set. The second input spatial mode is aligned with a detected output spatial mode of the first output spatial modes. Each single photon detector of multiple single photon detectors is disposed along a different one of the second output spatial modes from the second polarizing beam splitter. A first device output carries an output photon based in part on a number of photons detected by the single photon detectors. A polarizing beam splitter for a particular set of orthogonal polarizations transmits a photon that arrives on a particular input spatial mode with one polarization of the particular set onto one output spatial mode, and transmits a photon that arrives on the particular input spatial mode with a different polarization of the particular set onto a different output spatial mode.
The logic device is probabilistic, providing the correct output but only producing an output a fraction of the time. The fraction can be increased using post-detection operations that are based on which single photon detectors make detections. The fraction can be further increased using additional photon sources or linear components or both. By using beam splitters with different sets of orthogonal polarizations, photon polarization states associated with qubits are not measured during the detections of single photons, and photon state coherence is maintained during operation by the logic device.
In other aspects of the invention, a method of performing logic operations and a method of fabricating a logic device are presented.